The vectorial angle of a point P on the line joining the points (r1, θ1) and (r2, θ2) is then the length of radius vector of P is

Engineering

Mathematics

Introduction to Determinants

Question

The vectorial angle of a point P on the line joining the points (r₁, θ₁) and (r₂, θ₂) is $\frac{θ_{1} + θ_{2}}{2}$ then the length of radius vector of P is

$\frac{r_{1} - r_{2}}{r_{1} + r_{2}} \cos (\frac{θ_{1} - θ_{2}}{2})$

$\frac{r_{1} + r_{2}}{r_{1}, r_{2}} \cos (\frac{θ_{1} - θ_{2}}{2})$

$\frac{r_{1} r_{2}}{r_{1} + r_{2}} \cos (\frac{θ_{1} - θ_{2}}{2})$

None of these

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Given points are A(r₁, θ₁), B(r₂, θ₂)

Eq of line passing through two given points is given by:

y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})

∴ y - θ_{1} = \frac{θ_{2} - θ_{1}}{r_{2} - r_{1}} (x - r_{1})

Now, angle between point P and line is

\frac{θ_{1} + θ_{2}}{2}

Let point P meet at point Q on the line.

The radius will be R = Pcosθ

∴ R = PQcos (\frac{θ_{1} + θ_{2}}{2})

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